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Transcript
Topic 4 Engineering 1333: Electrical Circuits The Kirchhoff Laws (Sections 2.3 & 2.4) 9/16/20059/12/2007 Kirchoff Laws 1 A Circuit R1 Here’s a circuit with one voltage source and several resistors i4 + + vs R3 - We’d like to “solve” the circuit. That is we’d like to find out: (a) the voltage drop across each resistor or R4 v4 - Either will do since we can use Ohm’s Law to find the other For example v4 R4i4 (b) the current that flows through it. 9/16/2005 R2 Kirchoff Laws To do that we need to know how voltages and currents combine 2 The Kirchhoff Current Law + vs R1 R2 i1 i2 i3 Tee Junction R4 R3 - i2 i1 What goes in must come out i1 i2 i3 i3 9/16/2005 Kirchoff Laws 3 Effect of Reference Directions + vs R1 R2 i1 i2 i3 Arbitrarily changed current reference directions R4 R3 - What goes in must come out i2 i1 i3 i1 i2 i3 0 or i1 i2 i3 How many ways could we choose reference directions for this junction? 9/16/2005 Kirchoff Laws 8 4 In General i2 i1 At any node (a node is a point where two or more elements meet) i3 i4 The sum of the incoming currents = The sum of the outgoing currents i1 i2 i3 i4 9/16/2005 Kirchoff Laws 5 Alternatively i1 i4 i2 i3 The sum of all currents (treating incoming currents as positive and outgoing currents as negative) is zero i1 i2 i3 i4 0 9/16/2005 Kirchoff Laws 6 A Loop Start at any node trace a closed path through the circuit coming back to the original node without passing through any intermediate node more than once. There are 3 loops There are 4 nodes in the circuit below R2 R1 2 1 3 c + a vs b R3 R4 0 9/16/2005 Kirchoff Laws 7 Kirchhoff Voltage Law The algebraic sum of all voltages around any closed path (loop) in a circuit We need to assign some voltages v1 + R1 a - v3 v2 + R2 Take your best shot - …and let the algebra sort it out. + c R3 b Loop a R4 v4 - Loop c 9/16/2005 zero …but which way is uphill and which is downhill? + + vs - is Kirchoff Laws Loop b v1 v3 vs 0 v2 v4 v3 0 v1 v2 v4 vs 0 8 Improved Model for a Battery Voltage drops as current increases vo vB Ri io + vi io - Internal Resistance + + Ri vo vB - 9/16/2005 By KVL: Solving for vo: Applying Ohm’s Law: Kirchoff Laws vi vo vB 0 vo vB vi vo vB Riio 9